dorsal/arxiv
View SchemaThe Power of LOCCq State Transformations
| Authors | Ashish V. Thapliyal, John A. Smolin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0212098 |
| URL | https://arxiv.org/abs/quant-ph/0212098 |
| DOI | 10.1103/PhysRevA.68.062324 |
Abstract
Reversible state transformations under entanglement non-increasing operations give rise to entanglement measures. It is well known that asymptotic local operations and classical communication (LOCC) are required to get a simple operational measure of bipartite pure state entanglement. For bipartite mixed states and multipartite pure states it is likely that a more powerful class of operations will be needed. To this end \cite{BPRST01} have defined more powerful versions of state transformations (or reducibilities), namely LOCCq (asymptotic LOCC with a sublinear amount of quantum communication) and CLOCC (asymptotic LOCC with catalysis). In this paper we show that {\em LOCCq state transformations are only as powerful as asymptotic LOCC state transformations} for multipartite pure states. We first generalize the concept of entanglement gambling from two parties to multiple parties: any pure multipartite entangled state can be transformed to an EPR pair shared by some pair of parties and that any irreducible $m$ $(m\ge 2)$ party pure state can be used to create any other state (pure or mixed), using only local operations and classical communication (LOCC). We then use this tool to prove the result. We mention some applications of multipartite entanglement gambling to multipartite distillability and to characterizations of multipartite minimal entanglement generating sets. Finally we discuss generalizations of this result to mixed states by defining the class of {\em cat distillable states}.
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"abstract": "Reversible state transformations under entanglement non-increasing operations\ngive rise to entanglement measures. It is well known that asymptotic local\noperations and classical communication (LOCC) are required to get a simple\noperational measure of bipartite pure state entanglement. For bipartite mixed\nstates and multipartite pure states it is likely that a more powerful class of\noperations will be needed. To this end \\cite{BPRST01} have defined more\npowerful versions of state transformations (or reducibilities), namely LOCCq\n(asymptotic LOCC with a sublinear amount of quantum communication) and CLOCC\n(asymptotic LOCC with catalysis). In this paper we show that {\\em LOCCq state\ntransformations are only as powerful as asymptotic LOCC state transformations}\nfor multipartite pure states. We first generalize the concept of entanglement\ngambling from two parties to multiple parties: any pure multipartite entangled\nstate can be transformed to an EPR pair shared by some pair of parties and that\nany irreducible $m$ $(m\\ge 2)$ party pure state can be used to create any other\nstate (pure or mixed), using only local operations and classical communication\n(LOCC). We then use this tool to prove the result. We mention some applications\nof multipartite entanglement gambling to multipartite distillability and to\ncharacterizations of multipartite minimal entanglement generating sets. Finally\nwe discuss generalizations of this result to mixed states by defining the class\nof {\\em cat distillable states}.",
"arxiv_id": "quant-ph/0212098",
"authors": [
"Ashish V. Thapliyal",
"John A. Smolin"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.68.062324",
"title": "The Power of LOCCq State Transformations",
"url": "https://arxiv.org/abs/quant-ph/0212098"
},
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